Continuous fine-grain status monitoring of a cloud data center enables rapid response to anomalies, but handling the resulting torrent of data poses a significant challenge. As a solution, we propose CloudSense, a new switch design that performs in-network compression of status streams via compressive sensing. Using MapReduce straggler detection as an example of cloud monitoring, we give evidence that CloudSense allows earlier detection of stragglers, since finer-grain status can be reported for a given bandwidth budget. Furthermore, CloudSense showcases the advantage of an intrinsic property of compressive sensing decoding that enables detection of the slowest stragglers first. Finally, CloudSense achieves in-network compression via a low-complexity encoding scheme, which is easy and convenient to implement in a switch. We envision that CloudSense switches could form the foundation of a "compressed status information plane" that is useful for monitoring not only the cloud data center itself, but also the user applications that it hosts.